Yeah, it's responsive design, and when the page's width becomes too narrow the button simply disappears, as shown in the two screenshots I took.

However, I would say that it's a web design issue and not a real estate issue. Let me quote one article on the subject:

A bigger screen doesn’t mean that the user suddenly wants a cramped layout which is difficult to scan, nor does a smaller screen mean that the user would never request any kind of information that they’ve seen on the site before. Therefore, show the same content, but “package” it differently so that it is optimized for the screen it is being displayed on.

I'm not a web designer myself, but a suggestion is to put the feedback button in the hamburger menu when on mobile. My point though, is that it's irritating that a worse version of DuckDuckGo is served on mobile with fewer features (i.e. without the feedback button in this case). I understand that there's obviously less real estate to work with on a phone, but I'm sure a web designer would be able to work it out.

UI wise, you're both right, it's a real-estate issue. We considered adding it to the hamburger menu on mobile. It's not hard (we do it for the app link for example). The hard part is in the process of submitting feedback itself.

The only concrete feedback we've garnered from the feedback box to date is that we need to improve the feedback box / process :). We're going to focus on that first.

What I like about the feedback button on the search results page is that I'm able to give feedback on the quality of the results.

I remember that the previous feedback button was more explicitly for giving feedback on the results' quality, while this iteration appears to be slightly more general.

What I would like is just a simple button for reporting poor results, and a field where I can tell what I did expect to find. (However, I don't know if such submissions are useful for you.) Since I'm also doing searches on my phone, I would like to be able to give feedback there too whenever I have some seconds to spare.